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Introducing Oblique Asymptotes

Introducing Oblique Asymptotes. Horizontal Asymptote Rules: If numerator and denominator have equal highest power, simplified fraction is the H.A. If denominator has a higher power than the numerator the H.A. is zero What happens when the numerator has a higher power than the denominator?.

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Introducing Oblique Asymptotes

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  1. Introducing Oblique Asymptotes • Horizontal Asymptote Rules: • If numerator and denominator have equal highest power, simplified fraction is the H.A. • If denominator has a higher power than the numerator the H.A. is zero • What happens when the numerator has a higher power than the denominator?

  2. Rational Functions – Oblique Asymptotes • Oblique Asymptotes – Sometimes called slant asymptotes • Happens when the degree of the numerator is greater than the degree of the denominator.

  3. Rational Functions – Oblique Asymptotes • How to Graph a Rational Function that Contains an Oblique Asymptote • Find Vertical Asymptote Normal Way (set denominator = to zero) • Find roots the normal way (set entire function = to zero) • Find oblique asymptote • Divide numerator by denominator by either polynomial or synthetic division • Resulting quotient is oblique asymptote (ignore remainder. • Test zones as you normally would (are points above or below oblique asymptote?)

  4. Rational Functions – Oblique Asymptotes • Examples: • f(x) = x2 – x – 2 x – 1 • f(x) = x2 – x x + 1

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